A pre-rooted ROM for software version 5.0.5 for the Fire TV 2 has just been released by rbox. You can download it from here. This ROM also includes version 3.0.0-3 of TWRP recovery, so installing it will also update recovery to the latest version. If you’ve already rooted your Fire TV 2 using my guide, then all you need to do is install the ROM using TWRP. Instructions for that can be found here. If you haven’t rooted your Fire TV and want to install this ROM, simply follow my rooting guide and use the 5.0.5 ROM. There is no need to install older versions first. You can jump directly to 5.0.5 regardless of which software version is currently on your Fire TV 2.
Those of you with rooted 1st-gen Fire TVs should not use this ROM. It is only for the 2nd-gen Fire TV. Rbox still plans to release TWRP and a pre-rooted 5.0.5 ROM for the 1st-gen Fire TV.